Contribution
On the size of classes with weak membership properties

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Abstract

It is shown that the following classes have resource-bounded measure 0 in E: the class of P-selective sets, the class of P-multiselective sets, the class of cheatable sets, the class of easily countable sets, the class of easily approximable sets, the class of near-testable sets, the class of nearly near-testable sets, the class of locally self-reducible sets. These are corollaries of a more general result stating that the class of sets that are P-isomorphic to P-quasi-approximable sets has measure 0 in E. By considering the recent approach of Allender and Strauss for measuring in subexponential classes, we obtain similar results with respect to P for classes having weak logarithmic time membership properties.

Keywords

Resource-bounded measure
P-selective sets
P-multiselective sets
Cheatable sets
Easily countable sets
Easily approximable sets
Near-testable sets
Nearly near-testable sets
Locally self-reducible sets
P-bi-immune sets

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1

Supported in part by grant NSF-CCR-8957604, NSF-INT-9116781/JSPS-ENG-207 and NSF-CCR-9322513 and by the Romanian Department of Education and Science grant 4975-92. A preliminary version of this work has been presented at the 7th International Conference on Computing and Information, Peterborough, Canada, July 1995. Work done in part while at the University of Rochester.